Maximization of quadratic forms expressed by distance matrices

Saichi Izumino, Noboru Nakamura

Research output: Contribution to journal › Article

Abstract

If x, y, z are real numbers satisfying x + y + z = 1, then the maximum of the quadratic form axy + bxz + cyz with positive constants a, b, c is abc/2ab + 2ac + 2bc − a2 − b2 − c2 under the assumption √a < √b + √c. Extending this fact, we give the maximum of the quadratic form ∑1≤i<j≤n aijxixj in n-variables x1, …, xn satisfying ∑n i=1 xi = 1 with constants aij = 0 under certain assumptions.

Original languageEnglish
Pages (from-to)641-658
Number of pages18
JournalHokkaido Mathematical Journal
Volume35
Issue number3
DOIs
Publication statusPublished - Jan 1 2006
Externally publishedYes

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Distance Matrix
Quadratic form

Keywords

  • Distance matrix
  • Ozeki’s inequality
  • Quadratic form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Maximization of quadratic forms expressed by distance matrices. / Izumino, Saichi; Nakamura, Noboru.

In: Hokkaido Mathematical Journal, Vol. 35, No. 3, 01.01.2006, p. 641-658.

Research output: Contribution to journal › Article

Izumino, S & Nakamura, N 2006, 'Maximization of quadratic forms expressed by distance matrices', Hokkaido Mathematical Journal, vol. 35, no. 3, pp. 641-658. https://doi.org/10.14492/hokmj/1285766422
Izumino S, Nakamura N. Maximization of quadratic forms expressed by distance matrices. Hokkaido Mathematical Journal. 2006 Jan 1;35(3):641-658. https://doi.org/10.14492/hokmj/1285766422
Izumino, Saichi ; Nakamura, Noboru. / Maximization of quadratic forms expressed by distance matrices. In: Hokkaido Mathematical Journal. 2006 ; Vol. 35, No. 3. pp. 641-658.
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